Results & Lemmas (6)
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LEMMA 1.
LEMMA 1. Let II and D be regular in E, D map E onto a many sheeted starlike region,,7(0) = D(0) = 0, il' 0)/D' 0) = p, (l/p)[il'(z)/D'(z))…
LEMMA 1. Let II and D be regular in E , D map E onto a many sheeted starlike region, ,7(0) = D(0) = 0 , il'{0)/D'{0) = p , (l/p)[il'(z)/D'(z)) 6 P(A, B) . Then (l/p) (tf(s )/D(z)) I P(A, B) , p > 1 .
LEMMA 2
LEMMA 2 [2]. Let N and D be regular in E, D map E onto a many sheeted starlike region, N(0) = D 0) = 0, N'(0)/D'(0) = p, Re(N'(z)/D'(z)) >…
LEMMA 2 [2]. Let N and D be regular in E , D map E onto a many sheeted starlike region, N(0) = D{0) = 0 , N'(0)/D'(0) = p , Re(N'(z)/D'(z)) > 0 .
LEMMA 4.
LEMMA 4. Let f Z T. Then f Z S* B, A, B) if and only if
LEMMA 4. Let f Z T . Then f Z S*{B , A, B) if and only if
LEMMA 5.
LEMMA 5. Let £ € 2^. I%ew g'/a± € P(/l, B) if and only if (k) T B+±)- B-A)zm Q-^am SB - A.
LEMMA 5. Let £ € 2^ . I%ew g'/a± € P(/l, B) if and only if (k) T \m{B+±)-{B-A)zm Q-^am SB - A .
THEOREM 2.
THEOREM 2. Let g € S*[zQ, A, B) and f(z) = [z1~°/(p+c)) [z°g(z)~] ' Then f is p-valently starlike of order a. 3 0 S a < 1 t in the disc
THEOREM 2. Let g € S*[zQ, A, B) and f(z) = [z1~°/(p+c)) [z°g(z)~] ' Then f is p-valently starlike of order a. 3 0 S a < 1 t in the disc
THEOREM 3.
THEOREM 3. Let g £ T± and get g'la^ € P(A, B). Define https://doi.org/10.1017/S0004972700005438 Published online by Cambridge University…
THEOREM 3. Let g £ T± and get g'la^ € P(A, B) . Define https://doi.org/10.1017/S0004972700005438 Published online by Cambridge University Press
Function classes studied:
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